Answer
79 years.
Work Step by Step
From Appendix B, we see that the half-life of the strontium isotope is 28.90 years.
Use equations 30–5 and 30-6 to find the time for 85 percent to decay. At that time, the activity will be 15 percent of its initial value.
$$0.15R_0=R_0e^{-\lambda t}=R_0 e^{-\frac{ln 2}{T_{1/2}}t}$$
$$0.15= e^{-\frac{ln 2}{T_{1/2}}t}$$
$$ln(0.15)= -\frac{ln 2}{T_{1/2}}t$$
$$t=-\frac{T_{1/2}ln(0.15)}{ln 2}=-\frac{(28.90y)(ln(0.15))}{ln2}\approx 79y$$
